discuss centroids
diff --git a/site/src/site/blog/whisky-revisited.adoc b/site/src/site/blog/whisky-revisited.adoc
index 9acb41f..c1a1286 100644
--- a/site/src/site/blog/whisky-revisited.adoc
+++ b/site/src/site/blog/whisky-revisited.adoc
@@ -116,7 +116,9 @@
The highest correlations are between _Smoky_ and _Medicinal_, and _Smoky_ and _Body_.
Some, like _Floral_ and _Medicinal_, are very unrelated.
-Let's now explore searching for whiskies of a particular flavor,
+Groovy has a flexible syntax. Underdog has used this to piggyback on Groovy's list notation
+allowing column expressions for filtering data within a dataframe.
+Let's use column expressions to find whiskies of a particular flavor,
in this case profiles that are somewhat _fruity_ and somewhat _sweet_ in flavor.
[source,groovy]
@@ -235,8 +237,46 @@
2:AnCnoc, Ardmore, ArranIsleOf, Auchentoshan, Aultmore, Benriach, Bladnoch, Bunnahabhain, Cardhu, Craigallechie, Craigganmore, Dalwhinnie, Deanston, Dufftown, GlenDeveronMacduff, GlenElgin, GlenGrant, GlenKeith, GlenMoray, GlenSpey, Glenallachie, Glenfiddich, Glengoyne, Glenkinchie, Glenlossie, Glenmorangie, Inchgower, Linkwood, Loch Lomond, Mannochmore, Miltonduff, OldFettercairn, RoyalBrackla, Scapa, Speyburn, Speyside, Strathmill, Tamdhu, Tamnavulin, Tobermory, Tomatin, Tomintoul, Tomore, Tullibardine
----
-It's very hard to visualize 12 dimensional data,
-so let's project our data onto 2 dimensions using PCA and store those projections back into the dataframe:
+We might also be interested in the cluster centroids, i.e. the average flavor profiles
+for each cluster. Currently, Underdog uses Smile, under the covers,
+for clustering via K-Means. The Smile K-Means model already calculates the centroids
+but currently, that information is behind Underdog's simplified K-Means abstraction.
+
+Nevertheless, it isn't hard to recalculate the centroids ourselves:
+
+[source,groovy]
+----
+def summary = df
+ .agg(features.collectEntries{ f -> [f, 'mean']})
+ .by('Cluster')
+ .sort_values(false, 'Cluster')
+ .rename('Flavour Centroids')
+----
+
+We'll take the results and do some minor formatting changes:
+
+[source,groovy]
+----
+(summary.columns - 'Cluster').each { c ->
+ summary[c] = summary[c](Double, Double) {it.round(3) }
+}
+println summary
+----
+
+Which has this output:
+
+----
+ Mean flavor by Cluster
+ Cluster | Mean [Body] | Mean [Sweetness] | Mean [Smoky] | Mean [Medicinal] | Mean [Tobacco] | Mean [Honey] | Mean [Spicy] | Mean [Winey] | Mean [Nutty] | Mean [Malty] | Mean [Fruity] | Mean [Floral] |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+ 0 | 2.76 | 2.44 | 1.44 | 0.04 | 0 | 1.88 | 1.68 | 1.92 | 1.92 | 2.04 | 2.16 | 1.72 |
+ 1 | 2.529 | 1.647 | 2.765 | 2.118 | 0.294 | 0.647 | 1.647 | 0.588 | 1.353 | 1.412 | 1.353 | 0.941 |
+ 2 | 1.5 | 2.455 | 1.114 | 0.227 | 0.114 | 1.114 | 1.114 | 0.591 | 1.25 | 1.818 | 1.773 | 1.977 |
+----
+
+Looking at the centroids is one way to understand how the whiskies have been grouped.
+But, it's very hard to visualize 12 dimensional data, so instead,
+let's project our data onto 2 dimensions using PCA and store those projections back into the dataframe:
[source,groovy]
----
@@ -436,6 +476,27 @@
assert m.rows().countBy{ it.Cluster } == [0:51, 1:23, 2:12]
----
+The cluster centroids, i.e. the average flavor profiles
+for each cluster. These are available from the Smile model (we'll denormalize the values
+by multiplying by 4, and then pretty print them to 3 decimal places):
+
+[source,groovy]
+----
+println 'Cluster ' + features.join(' ')
+model.centers().eachWithIndex { c, i ->
+ println " $i: ${c*.multiply(4).collect('%.3f'::formatted).join(' ')}"
+}
+----
+
+Which has this output:
+
+----
+Cluster Body Sweetness Smoky Medicinal Tobacco Honey Spicy Winey Nutty Malty Fruity Floral
+ 0: 1.569 2.392 1.235 0.294 0.098 1.098 1.255 0.608 1.235 1.745 1.784 1.961
+ 1: 2.783 2.435 1.478 0.043 0.000 1.913 1.652 2.000 1.957 2.087 2.174 1.696
+ 2: 2.833 1.583 2.917 2.583 0.417 0.583 1.417 0.583 1.500 1.500 1.167 0.583
+----
+
We can also project onto two dimensions using Principal Component Analysis (PCA).
We'll again use the
https://haifengl.github.io/feature.html#dimension-reduction[Smile] functionality for this.
